jmc

$175=5^2\cdot 7^1$. To arrange the divisors of 175, we can (conveniently) start with the divisor 7. Since $\gcd (5,7)=1$, the two divisors that are adjacent to 7 must be multiples of 7, which means they have to be $5^1\cdot 7=35$ and $5^2\cdot 7=175$. Thus, the sum of the two integers adjacent to 7 is $35+175=\boxed{210}$.